1. Field of the Invention
The present invention relates in general to the field of information processing, and more specifically to a system and method for reducing near out-of-band noise using a delta sigma modulator and a finite impulse response post-processing filter.
2. Description of the Related Art
Many electronic systems employ signal processing technology to process analog, digital, or a mix of analog and digital signals. In audio applications, the digital to analog conversion process often involves oversampling a digital signal, modulating the signal using a delta-sigma modulator to shape noise associated with quantizing the digital signal, and performing a digital to analog conversion using a low-pass filter. The filtered output signal is used in a variety of ways, such as stored as digital data or amplified to produce an analog signal suitable for driving a load such as a speaker.
Delta-sigma modulators receive an input signal and convert the signal into a series of low resolution pulses having an average amplitude over time proportional to the input signal. In the process of producing a modulated output signal, delta-sigma modulators introduce quantization noise into the modulated input signal. However, the quantization noise advantageously resides outside of the audio baseband where frequency components of interest reside, i.e. between about 0 Hz and about 20-25 kHz. Thus, in an audio context, “in-band” refers to frequencies between 0 Hz and about 20-25 kHz, and out-of-band frequencies refer to frequencies above the maximum in-band frequency. “Delta-sigma modulators” are also commonly referred to using other interchangeable terms such as “sigma-delta modulators”, “delta-sigma converters”, “sigma delta converters”, “data converters”, “noise shapers”, as well as full and partial combinations of the foregoing terms.
FIG. 1 depicts a signal processing system 100 that converts an input signal 101 generated by source 102 into an output signal 104. The source 102 can be any data signal source such as a compact disk player, a digital versatile disk player, and other audio signal sources. The input signal 101 generally undergoes pre-processing by preprocessor 106. In an audio system context, in preparation for processing by delta sigma modulator 108, pre-processing generally involves over-sampling input signal 101. Thus, for an audio signal sampled at 48 kHz and an oversampling ration of 128:1, pre-processor 106 generates an input signal x(n) (“X(z)” in the z-domain) with a sampling frequency of 6.144 MHz.
The M-bit delta sigma modulator 108 represents a general depiction of an M-bit delta sigma modulator. The delta sigma modulator 108 provides a series of low resolution pulses whose average value over time represents delta sigma modulator input signal X(z), where M is an integer representing the number of bits used by the delta sigma modulator 108 to quantize an input to quantizer 110. For a single bit delta sigma modulator 110, M equals one (1). The loop filter 112 output signal U(z) is related to the input signal X(z) and the feedback signal Y(z)·z−1 by Equation [1]:U(z)=X(z)·H1(z)+Y(z)·H2(z)·z−1  [1]
Because delta sigma modulator 108 introduces quantization error noise E(z) at the quantizer 110, the loop filter 112 can be characterized by two transfer functions: (i) a signal transfer function (STF) and (ii) a noise transfer function (NTF). The STF(z) is related to H1(z) and H2(z) by Equation [2], and the NTF(z) is related to H2(z) by Equation [3]:
                                          STF            ⁡                          (              z              )                                =                                                    H                1                            ⁡                              (                z                )                                                    1              -                                                z                                      -                    1                                                  ·                                                      H                    2                                    ⁡                                      (                    z                    )                                                                                      ;                            [        2        ]                                                      NTF            ⁡                          (              z              )                                =                      1                          1              -                                                z                                      -                    1                                                  ·                                                      H                    2                                    ⁡                                      (                    z                    )                                                                                      ,                            [        3        ]            
Each NTF has a numerator and a denominator. “Zeros” represent roots of the NTF numerator that cause the NTF to equal zero or at least a very small number that for practical purposes approximates zero (collectively referred to herein as a “zero”). “Poles” represent roots of the NTF denominator that cause the NTF to equal infinity (e.g. a division by zero) or at least a very large number that for practical purposes approximates infinity or a maximum voltage or current swing of a system.
FIG. 2 depicts a 5th order delta sigma modulator 200, which is an embodiment of delta sigma modulator 108. The loop filter 202 includes 5 integrators 204.0, 204.1, . . . , 204.4. Filter coefficients ci to obtain a desired STF and NTF can be, for example, included in the feedback loop. The feedback signal Y(z)·z−1 (i.e. the previous output y(n−1)) is fed back and, thus, modified by a coefficient ci, where iε{0, 1, . . . , 4}. The values of each coefficient ci are a matter of design choice. Integrator 204.0 integrates the difference between input signal X(z) and a delayed quantizer output feedback signal Y(z)·z−1 as modified by coefficient c0. Integrators 204.2 and 204.4 integrate a difference between Y(z)·z−1, as adjusted by respective coefficients c2 and c4, and an output of the respective previous integrator 204.1 and 204.3. Resonators 208 and 210 provide poles in the transfer function of loop filter 202. Resonators 208 and 210 have respective gains −g0 and g1. The values of −g1 and −g2 are a matter of design choice. Integrator 204.1 integrates −[c1·Y(z)·z−1+g0·V2(z)]+V0(z), where Vi(z) is the output of the ith integrator 204. Integrator 204.3 integrates −[c3·Y(z)·z−1+g1·V4(z)]+V2(z). The ith integrator 204.i performs a process that determines a difference between an input A(z) and a delayed integrator output B(z) such that the integrator transfer function, H(z)integrator, is represented by Equation [1]:
                                          H            ⁡                          (              z              )                                integrator                =                                            A              ⁡                              (                z                )                                                    B              ⁡                              (                z                )                                              =                      1                          1              -                              z                                  -                  1                                                                                        [        1        ]            
The quantizer 206 produces a quantization error E(z), which represents noise produced by the delta sigma modulator 200. The Nth order delta sigma modulator output signal Y(z) can be defined in terms of the input signal X(z), the error E(z), the STF of the loop filter 202, and the NTF of the loop filter 202 as set forth in the z-domain Equation [5]:Y(z)=STF(z)·X(z)+NTF(z)·E(z)  [5]For loop filter 202, STF(z) is an all pole response that is relatively flat in the in-band frequencies and rolls off at higher frequencies, and NTF(z)=(1−z−1)N. Delta sigma modulators can be implemented using a vast array of configurations that are well discussed extensively in the literature such as Delta Sigma Data Converters—Theory, Design, and Simulation, Norsworthy, Schreier, and Temes, IEEE Press (1997) and Understanding Delta-Sigma Data Converters, Schreier and Temes, IEEE Press (2005).
FIG. 3 depicts an exemplary 5th order NTF 300 in the z-domain. The five zeros (“0”) of the NTF 300 are separated within the in-band frequencies, and the five poles (“X”) are located within the unit circle surrounding the in-band frequencies. Understanding Delta-Sigma Data Converters states, “Spreading the zeros reduces the total noise power in the signal band, while moving the poles nearer to the zeros reduces the out-of-band NTF gain, resulting in improved stability.” Understanding Delta-Sigma Data Converters, p. 107.
FIG. 4 depicts the frequency response 400 of the 5th order NTF 300. The frequency response 400 exhibits a steep rise, i.e. a steep decline in attenuation, after the baseband frequency fb.
Referring back to FIG. 1, the signal processing system 100 also includes post-processor 114 to prepare the output signal Y(z) for one or more output devices, such as audio speakers or an audio data storage device. Post-processor 114 processes the output signal Y(z) of delta sigma modulator 108 to prepare output signal Y(z) for its intended use. Post-processor 114 often includes a digital-to-analog converter and a low-pass filter which largely remove out-of-band noise from the output signal Y(z) to generate the output signal 104. Near out-of-band noise is very difficult to remove. Attempts to remove near out-of-band noise generally involve multi-stage filters and large capacitors. However, near out-of-band energy remains and can cause a variety of undesirable effects. For example, subsequent signal processing of a signal with near out-of-band noise can introduce modulation frequencies that modulate the near out-of-band energy back into in-band frequencies, thus, introducing in-band noise. For example, jitter modulation commonly exists in decoders decoding Sony-Philips Digital Interface Format (SPDIF) signals. The jitter modulation can problematically modulate the near out-of-band energy back into the in-band frequencies, thus, introducing unwanted noise. In addition to modulation of near out-of-band noise into in-band frequencies, near out-of-band noise can cause other problems as well. For example, some audio amplifiers do not function satisfactorily when near out-of-band noise is present in a signal to be amplified.